Getting Started 
Misconception/Error The student is unable to envision the threedimensional shape that results and only describes a twodimensional shape. 
Examples of Student Work at this Level The student writes the coordinates of points of the image reflected about the given axis.
The student writes a statement such as:
 The solid is a triangle.
 It will form a diamond.
 The triangle will be upside down.
 It would form a circle.

Questions Eliciting Thinking What is a threedimensional shape or solid?
How is a threedimensional solid formed from the rotation of a twodimensional figure? 
Instructional Implications Be sure the student understands the distinction between two and threedimensional figures. Discuss a variety of real world examples of rotational motion to help the student visualize threedimensional solids, e.g. a spinning quarter, a hand mixer, an airplane propeller.
Help the student visualize the solids formed by attaching the edge of a right triangle to the side of a thin straw. Have the student hold the straw horizontally while slowly, and then more quickly, rolling the straw between his or her palms, modeling the desired rotation. Have the student repeat this exercise with a variety of twodimensional shapes whose dimensions are given. Have the student identify the solid formed by the rotation of each of these shapes, also describing their dimensions.
Demonstrate the solids formed by the rotation of twodimensional shapes by using interactive websites such as “3D Transmographer” (shodor.org). 
Moving Forward 
Misconception/Error The student is able to visualize one or both of the first two solids of rotation as threedimensional, but identifies and/or describes one or both of the solids incorrectly. 
Examples of Student Work at this Level The student writes a statement such as:
 The solid is a pyramid.
 The solid is a cone. (dimensions are incorrect)
 The solid is shaped like a spinning top.
 The solid is a 3D shape.
 The solid is a prism.

Questions Eliciting Thinking Describe to me what this solid looks like.
Can you describe the base of the solid?
What are the dimensions of the solid?
How do the dimensions of the solid differ when rotated around the yaxis versus the xaxis?
To what point on the xaxis/yaxis does the base of the solid extend? 
Instructional Implications Help the student visualize the solids formed by attaching the edge of a right triangle to the side of a thin straw. Have the student slowly, and then more quickly, roll the straw between his or her palms to model the desired rotation. The student can repeat this exercise with a variety of twodimensional shapes.
Have the student identify the solid formed by the rotation of each of these shapes, describing the dimensions, if given. 
Almost There 
Misconception/Error The student struggles to identify the solid formed by rotating the triangle around a line that does not contain one of its sides. 
Examples of Student Work at this Level The student accurately identifies the solids of rotation and their dimensions for the first two problems. For the third problem, the student writes a statement such as:
 The solid is a cylinder.
 The solid looks like a hole.
 The solid looks like a cup or bowl.
 The solid would be formed by a reverse cone going inward.

Questions Eliciting Thinking Can you describe the solid formed by this right triangle rotating about x = 2.
What are the dimensions of the cylinder that you are visualizing?
When rotated about x = 2, what solid is formed by the hypotenuse of the right triangle?
Can you describe the shape of the “hole” in the cylinder? 
Instructional Implications Demonstrate the solids formed by the rotation of twodimensional shapes by using interactive websites such as “3D Transmographer” (shodor.org). Then provide the student with additional problems similar to those in this task in which the student must visualize and describe the result of the rotation.
Consider implementing MFAS task 2D Rotations of Rectangles (GGMD.2.4). 
Got It 
Misconception/Error The student provides complete and correct responses to all components of the task. 
Examples of Student Work at this Level The student writes a statement such as, “The solid in question 1 is a cone with a height of 3 units and a circular base with a diameter of 4 units. The solid in question 2 is also a cone. Its height is 2 units with a circular base with a diameter of 6 units. The solid in question 3 is a cylinder with an inverted cone removed. The height of both the cylinder and the cone is 3 units and the diameter of their bases is 4 units. 
Questions Eliciting Thinking Where is the vertex of the cone in relation to the base of the cylinder?
How does the base of the cone compare to the base of the cylinder?
How does the height of the cone compare to the height of the cylinder?
Can you describe the solid formed by rotating the same right triangle about the line x = 2, y = 2, or y = 2? 
Instructional Implications Review the formulas for volume of a cone. Have the student compute and compare the volumes of the cones in questions 1 and 2.
Challenge the student to calculate the volume of the solid in question 3. 